a Multiply the numerator and denominator separately, then search for common factors.
B
b When dividing two fractions, the numerator is multiplied by the reciprocal of the denominator.
A
a 3/7
B
b 5/4
Practice makes perfect
a When multiplying fractions, the numerators and denominators are multiplied separately.
2/3* 9/14 = 2* 9/3* 14
We could determine each product, but let's first see if we can reduce the result. Since 9 and 3 have the common factor 3, so we can divide both the numerator and the denominator by 3.
2* 9/3* 14 = 2* 3/14
Since 14 is an even number one of its factors is 2, so we can further reduce our result by dividing the numerator and the denominator by 2.
2* 3/14 = 3/7
3 and 7 have no common factors so the fraction is in its simplest form. Now we can check our answer with a calculator.
Both 23* 914 and 37 gives the same result. This means our simplification is correct.
b The division of two fractions can be rewritten as a multiplication of the numerator and the reciprocal of the denominator.
3/5Ă· 12/25=3/5*25/12=3*25/5* 12
Both 3 and 5 are factors in 12 and 25. Therefore, we can divide the numerator and the denominator with both 3 and 5.
3*25/5* 12=25/5*4=5/4
5 and 4 have no common factors, so we've simplified the fraction as much as possible. Let's check our answer with a calculator.
We get the same result for both expressions, so the simplification is correct.
